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A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $\eta > 0$.
Orthogonal polynomials , volume 23
Gábor Szegő · 1939
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Criteria for recurrence and existence of invariant measures for multidimensional diffusions
RN Bhattacharya · 1978
Earlier work this paper cites.
Diffusions hypercontractives
Dominique Bakry and Michel Émery · 1985
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Isoperimetric problems for convex bodies and a localization lemma
Ravi Kannan, László Lovász, and Miklós Simonovits · 1995
Earlier work this paper cites.
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Mark Jerrum and Alistair Sinclair · 1996
Earlier work this paper cites.
Exponential convergence of Langevin distributions and their discrete approximations
Gareth O Roberts and Richard L Tweedie · 1996
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Concentration of measure and logarithmic Sobolev inequalities
Michel Ledoux · 1999
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Monte Carlo statistical methods , volume 2
Christian P Robert and George Casella · 1999
Cited alongside, same era.
Monte Carlo strategies in scientific computing , volume 10
Jun S Liu · 2001
Cited alongside, same era.
An introduction to MCMC for machine learning
Christophe Andrieu, Nando De Freitas, Arnaud Doucet, and Michael I Jordan · 2003
Cited alongside, same era.
Spectral gap and concentration for some spherically symmetric probability measures
Sergey G Bobkov · 2003
Cited alongside, same era.
Introductory lectures on convex optimization: A basic course , volume 87
Yurii Nesterov · 2003
Cited alongside, same era.
Asymptotic Geometric Analysis, Part I , volume 202
Shiri Artstein-Avidan, Apostolos Giannopoulos, and Vitali D Milman · 2015
Cited alongside, same era.
High dimensional statistics
Phillippe Rigollet and Jan-Christian Hütter · 2015
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NIST Digital Library of Mathematical Functions
DLMF · 2019
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Rapid convergence of the unadjusted Langevin algorithm: Isoperimetry suffices
Santosh Vempala and Andre Wibisono · 2019
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Probability and Random Processes
Geoffrey Grimmett and David Stirzaker · 2020
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Log-Concave Sampling
Sinho Chewi · 2022
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Resolving the mixing time of the Langevin Algorithm to its stationary distribution for log-concave sampling
Jason M. Altschuler and Kunal Talwar · 2023
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